a/c compressor very strange issue, can anyone help with this?

So this is actually on my tractor. It has a auto a/c setup. The issue is the compressor will not engage clutch. Now here is what is not understanding. There is 1 wire coming out of the compressor and connected to the wire coming from thermostat and on/off. Taking the connector loose I get 12v coming in but no clutch engagement. I can take a wire from +terminal from battery to wire at connector going in to the compressor and clutch will engage. connect wires back together and not engaged.
So, getting 12v going to compressor but clutch won't engage. disconnect wire and wire from battery clutch engages?????
Anyone, any ideas???
Thanks!

You need to measure for 12v with the compressor connected. If you don't have the 12v work your way backwards. The next step may be a low pressure switch and then to the thermostat.
Something in the path is not allowing the full compressor current to flow.

Your compressor clutch needs several amps of flow to get 12v. Your meter needs 0 amps to read full volts.